An elevator system requires a normal terminal stopping arrangement for an elevator car which is independent of the normal slowdown and stopping arrangement for the car. Thus, if the normal slowdown and stopping arrangement is calling for an operation which will cause the car to approach a terminal floor at an excessive speed, the normal terminal stopping arrangement will automatically override the normal slowdown and stopping arrangement, reducing the speed of the car according to a predetermined deceleration schedule, to stop the car smoothly at the terminal floor. The normal terminal slowdown function will hereinafter be referred to as TSD, for "Terminal Slow Down". Also, some additional emergency terminal device must be used. For example, with reduced stroke buffers, an emergency terminal speed limiting device must be used which is independent of any other emergency related device. This same emergency device, termed ETS for "Emergency Terminal Stop", may be used in elevator systems which have normal stroke buffers. The present invention is related to TSD, not ETS, and is thus related to apparatus for automatically overriding the normal slowdown and stopping control of an elevator car, when the normal slowdown control is malfunctioning, to smoothly stop the car at a terminal floor without exceeding predetermined values of deceleration and/or jerk.